Towards a Quantum Bag Dynamics (III)–Collective Motion of the Bag

Abstract

It is showed, that under the adiabatic assumption, the quark-gluon state and the energy of a dynamic bag may be expressed as functions of its collective coordinates and their first time derivatives. The effective Lagrangian and Hamiltonian for the collective motion are then proposed. The classical equation of collective motion is suggested to be used as the self-consistent equation for the force function . The bag dynamics is once again quantized. A set of ellipsoids and their finite combinations is recommended as a complete set of bag shapes because of its Lorentz invariance. The wave function for the internal motion of a hadron is therefore a function of the bag shape configuration. It may be used to average intrinsic observables and matrix elements of a hadron over the shape configuration. The zero momentum eigenstate of a hadron is constructed by making use of its translational symmetry. Finite momentum eigenstates are then constructed by Lorentz boosts. Multi-hadron states and hadron interactions are also considered.